Changes between Version 1 and Version 3 of Ticket #31991


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Timestamp:
06/16/21 17:35:24 (13 months ago)
Author:
gh-honglizhaobob
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  • Ticket #31991 – Description

    v1 v3  
    99Ideally after the implementation of this ticket, users can specify a fixed rank tensor for a general manifold using `tensor.modules`, specify a ring and a frame, and perform useful and normally computationally intractable tasks using tensor train as a backend. Based on the progress of this ticket, one may also consider implementing other backends for storing a numerical tensor such as tensor rings and quantized tensor train.
    1010
     11For alternative tensor decomposition formats, please see the following survey papers:
     12
     13- Tucker format: (https://arxiv.org/abs/1810.01262)
     14- Tensor ring: (https://arxiv.org/abs/1807.02513)
     15- Quantized tensor train (see section 3.5.1): (https://refubium.fu-berlin.de/handle/fub188/3366)
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    1117For the theory behind why one can reduce a normally exponential (in the number of dimensions) task to a linear task, see (https://epubs.siam.org/doi/abs/10.1137/090752286?journalCode=sjoce3).